Question

Dancers experience large forces associated with the jumps they make. For example, when a dancer lands after a vertical jump, the force exerted on the head by the neck must exceed the head’s weight by enough to cause the head to slow down and come to rest. The head is about 9.4% of a typical person’s mass. Video analysis of a 65-kg dancer landing after a vertical jump shows that her head decelerates from 4.0 m/s to rest in a time of 0.20 s. What is the magnitude of the average force that her neck exerts on her head during the landing? (a) 0 N; (b) 60 N; (c) 120 N; (d) 180 N.

Answer 1

(d) 180 N

Step-by-step explanation:

Head is joined with neck with the help of muscles which act as spring.

During jump , head presses the spring downward and gets stopped after a while .

weight of head = 65 x .094

= 6.11 kg

If R be the force, neck is exerting on head to stop it

net force on the head = R - mg

deceleration = 0 - 4 / 0.2

= - 20 m/s²

So (R-mg) / 6.11 = 20

R - 6.11 x 9.8 = 20 x 6.11

R = 122.2 + 60

= 182 N

= 180 N